Millions of packages per year are handled and shipped by United Parcel Service, Federal Express, and many other smaller courier and delivery services. These packages originate with federal, state, and local governments as well as private businesses of all sizes. In many instances, the charges by the carriers to their customers are based on the so-called “dim-weight factor” or “dimensional weight factor” (DWF) of the article being shipped, a fictitious dimension based on length (L) times width (W) times height (H) in inches divided by a standard agency or association-recognized divisor or conversion factor, commonly 139 (L×W×H)/139) for international shipments and 166 (L×W×H)/166) for domestic U.S. shipments. The “139” and “166” divisors or conversion factors have been recognized and adopted by the International Air Transport Association (I.A.T.A.). Even if an object or package is of irregular configuration, the “dim weight,” using the longest measurement each of length, width, and height, is still utilized for billing purposes. The volume computed by multiplication of object length, times width, times height may hereinafter be termed the “cubic volume,” “spatial volume,” or simply the “cube” of the object.
The measurements of the articles shipped are also critical so that the carrier can compute volume-based shipping charges; accurately determine the number of containers, trucks, trailers, or other vehicles required to transport goods to their destinations; and handlers of goods can optimize the use of space in retail as well as warehouse/distribution-center facilities. In addition, article weight and measurements may also be used to determine and predict weight and balance for transport vehicles and aircraft and to dictate the loading sequence for objects by weight and dimensions for maximum safety and efficiency. If orders of any items are to be packed into boxes, knowledge of object weight